Impressive result by Alex Smith!
Funny though how Wolfram's web sites on this
print Wolfram's name in larger font and more
frequently than Smith's, even trying to sell this
as New Kind Of Science although it's just a
continuation of a decades-old search for
small universal Turing machines :-)
Hi Max,
in this particular universe it's going well, thank you!
As promised, I had a look at your paper. I think
it is well written and fun to read. I've got a few comments
though, mostly on the nature of math vs computation,
and why Goedel is sexy but not an issue
when it comes to identifying
Dear colleagues,
many interesting talks
at the Zuse Symposium:
Is the universe a computer?
Berlin Nov 6-7, 2006
http://www.dtmb.de/Aktuelles/Aktionen/Informatikjahr-Zuse/
Best regards,
-JS
http://www.idsia.ch/~juergen/computeruniverse.html
--~--~-~--~~~---~--~~
. Technical issues and limits of computable
universes are discussed in papers available at:
http://www.idsia.ch/~juergen/computeruniverse.html
Even stronger predictions using a prior based
on the fastest programs (not the shortest):
http://www.idsia.ch/~juergen/speedprior.html
-Juergen Schmidhuber
inductive sciences, some of the results
are relevant not only for AI and computer science but also for
physics, provoking nontraditional predictions based on Zuse's
thesis of the computer-generated universe.
Comments welcome!
Juergen Schmidhuberhttp://www.idsia.ch/~juergen/
)...
Ed Clark has a nice review page on Wolfram's book:
http://www.math.usf.edu/~eclark/ANKOS_reviews.html
It includes Scott Aaronson's interesting review which also
addresses the issue of Bell's inequality.
Best,
Juergen http://www.idsia.ch/~juergen/digitalphysics.html
Juergen Schmidhuber
I welcome feedback on a little web page on Zuse's 1967 thesis
(which states that the universe is being computed on a cellular automaton):
http://www.idsia.ch/~juergen/digitalphysics.html
Juergen Schmidhuber
[EMAIL PROTECTED] wrote:
as for your point in your post about wheeler attaching
his name to the theory, I think its ok for proponents
and not originators of a theory to be named along with it.
for example lately Ive been referring to the
fredkin-wolfram thesis. fredkin is far more the
COLT paper may be old news to some
on this list.
--
The Speed Prior: a new simplicity measure yielding near-optimal
computable predictions (Juergen Schmidhuber, IDSIA)
In J. Kivinen and R. H. Sloan, eds, Proc. 15th
that
does not depend on output size.
Juergen Schmidhuber http://www.idsia.ch/~juergen/
Wei Dai wrote:
BTW, isn't the justification for universal prediction taken in this paper
kind of opposite to the one you took? The abstract says The problem,
however, is that in many cases one does not even have a reasonable guess
of the true distribution. In order to overcome this problem
Bill Jefferys wrote:
At 10:59 AM +0200 4/3/02, Juergen Schmidhuber wrote:
The theory of inductive inference is Bayesian, of course.
But Bayes' rule by itself does not yield Occam's razor.
By itself? No one said it did. Of course assumptions must be made.
At minimum one always has to choose
Bill Jefferys wrote:
At 9:19 AM +0100 3/27/02, Juergen Schmidhuber wrote:
You are claiming the AP necessarily implies a specific fact about
nuclear energy levels? I greatly doubt that - can you give a proof?
Yes, I can.
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1954ApJS
Bill Jefferys wrote:
It's pointless wasting my time on this. As both Russell and I pointed
out, this is a standard example that is cited by people who are
knowledgeable about the AP. Either you have a different definition of
predictive power than the rest of us do, or you don't understand
of CS: www.idsia.ch/~marcus
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
Wei Dai wrote:
I don't understand how you can believe that the probability of more
dominant priors is zero. That implies if I offered you a bet of $1
versus your entire net worth that large scale quantum computation will
in fact work, you'd take that bet. Would you really?
Your dollar
Prior might do so too.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
Wei Dai wrote:
On Thu, Nov 15, 2001 at 10:35:58AM +0100, Juergen Schmidhuber wrote:
Why do you prefer the Speed Prior? Under the Speed Prior, oracle universes
are not just very unlikely, they have probability 0, right? Suppose one
day we actually find an oracle for the halting problem
Wei Dai wrote:
Thanks for clarifying the provability issue. I think I understand and
agree with you.
On Tue, Nov 13, 2001 at 12:05:22PM +0100, Juergen Schmidhuber wrote:
What about exploitation? Once you suspect you found the PRG you can use
it
to predict the future. Unfortunately
Wei Dai wrote:
On Wed, Oct 31, 2001 at 10:49:41AM +0100, Juergen Schmidhuber wrote:
Which are the logically possible universes? Tegmark mentioned a
somewhat
vaguely defined set of ``self-consistent mathematical structures,''
implying provability of some sort. The postings of Marchal
of unprovable
aspects.
But why should this lack of provability matter? Ignoring this universe
just implies loss of generality. Provability is not the issue.
Juergen Schmidhuber
http://www.idsia.ch/~juergen/
http://www.idsia.ch/~juergen/everything/html.html
http://www.idsia.ch/~juergen/toesv2/
From: Russell Standish [EMAIL PROTECTED]
The only reason for not accepting the simplest thing is if it can be
shown to be logically inconsistent. This far, you have shown no such
thing, but rather demonstrated an enormous confusion between measure
and probability distribution.
From: Juho Pennanen [EMAIL PROTECTED]
So there may be no 'uniform probability distribution' on the set of all
strings, but there is the natural probability measure, that is in many
cases exactly as useful.
Sure, I agree, measures are useful; I'm using them all the time. But in
general they
Schmidhuber:
It's the simplest thing, given this use of mathematical
language we have agreed upon. But here the power of the
formal approach ends - unspeakable things remain unspoken.
Marchal:
I disagree. I would even say that it is here that the serious formal
approach begins. Take unprovable
Hi Max,
2) If so, should we really limit ourself to this particular kind
of mathematical structures? My concern is that we may be a bit too
narrow-minded if we do.
But this sort of narrow-mindedness seems necessary to remain within the
formally describable realm. I'd go beyond computable
Step n owns 2^(n-1) initial segments.
Bruno, why are we discussing this? Sure, in finite time you can compute
all initial segments of size n. In countable time you can compute one
real, or a countable number of reals. But each of your steps needs more
than twice the time required by the
those necessary
to explain the data. Observed data does not require more than a finite
number of bits, and never will.
Non-computability is not a restriction. It is an unnecessary extension
that greatly complicates things, so much that we cannot even talk about
it in a formal way.
Juergen
razor.
Juergen
Juergen Schmidhuber www.idsia.ch
Bruno:
Honestly it is still not clear. How could ever S(U)=TRUE be computable ?
As a computer scientist I guess you know that even the apparently simple
question does that piece of code computes the factorial function is not
computable.
Sure, it's not even decidable in general whether a
Bruno wrote:
I don't take the notion of observer for granted.
Neither do I, of course. The observer O is something computable that
evolves in some universe U.
The problem is that to be in a universe has no clear meaning
But it does. There is a computable predicate S such that S(U)=TRUE if
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